Ultrashort pulse propagation in high gain optical fiber amplifiers with normal dispersion is studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. An exact asymptotic solution is found, corresponding to a linearly chirped parabolic pulse which propagates self-similarly subject to simple scaling rules. The solution has been confirmed by numerical simulations and experiments studying propagation in a Yb-doped fiber amplifier. Additional experiments show that the pulses remain parabolic after propagation through standard single mode fiber with normal dispersion.

A broad class of exact self-similar solutions to the nonlinear Schrödinger equation (NLSE) with distributed dispersion, nonlinearity, and gain or loss has been found. Appropriate solitary wave solutions applying to propagation in optical fibers and optical fiber amplifiers with these distributed parameters have also been studied. These solutions exist for physically realistic dispersion and nonlinearity profiles in a fiber with anomalous group velocity dispersion. They correspond either to compressing or spreading solitary pulses which maintain a linear chirp or to chirped oscillatory solutions. The stability of these solutions has been confirmed by numerical simulations of the NLSE.

Pulse propagation in high-gain optical fiber amplifiers with normal group-velocity dispersion has been studied by self-similarity analysis of the nonlinear Schrödinger equation with gain. For an amplifier with a constant distributed gain, an exact asymptotic solution has been found that corresponds to a linearly chirped parabolic pulse that propagates self-similarly in the amplifier, subject to simple scaling rules. The evolution of an arbitrary input pulse to an asymptotic solution is associated with the development of low-amplitude wings on the parabolic pulse whose functional form has also been found by means of self-similarity analysis. These theoretical results have been confirmed with numerical simulations. A series of guidelines for the practical design of fiber amplifiers to operate in the asymptotic parabolic pulse regime has also been developed.

Self-similarity techniques are used to study pulse propagation in a normal-dispersion optical fiber amplifier with an arbitrary longitudinal gain profile. Analysis of the nonlinear Schrödinger equation that describes such an amplifier leads to an exact solution in the high-power limit that corresponds to a linearly chirped parabolic pulse. The self-similar scaling of the propagating pulse in the amplifier is found to be determined by the functional form of the gain profile, and the solution is confirmed by numerical simulations. The implications for achieving chirp-free pulses after compression of the amplifier output are discussed.

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